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Heat and Mass Transfer of Dusty Casson Fluid over a Stretching Sheet

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Abstract

Tiny particles in the Earth's atmosphere create dust that originates from various sources, including air pollution. The resulting dust contains numerous dust particles, and the size of these dust particles is sometimes homogeneous or irregular. The presence of dust in any kind of fluid in nature is a normal thing and this matter can no longer be ignored. Considering this fact, heat and mass transfer of the dusty Casson fluid flow over a permeable stretching sheet is investigated incorporating heat dissipation, magnetic and radiative fields, heat source or sink, and the effect of temperature gradient referred to as Dufour effect and thermophoresis stated as Soret effect. In this research, similarity analysis is used to transform the nonlinear governing partial differential equations into a set of nonlinear ordinary differential equations (ODE). Then the nonlinear ODE systems have been formulated using the finite difference method with the central difference technique and then solved. In addition, a comparison with other research findings is presented, which yields a quantitatively good agreement. Results revealed that the Eckert number, surface temperature parameter, conduction-radiation parameter, and Dufour effect lead to a substantial increase in the fluid flow rate and fluid temperature, the temperature of the dust particles, and momentum and thermal boundary layers. The magnitude of the drag coefficient becomes stronger with the augmentation of the Hartmann number, the mass concentration of dust particles, and the suction parameter. Moreover, an increase in the surface temperature parameter, conduction-radiation parameter, mass concentration of dust particles, and non-Newtonian Casson fluid parameter enhances the local Nusselt number.

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Abbreviations

B 0 :

Magnetic field parameter

\(C\) :

The concentration of the fluid

\(C_{p}\) :

Specific heat of the fluid

\(C_{m}\) :

Specific heat of the dust particles

\(C_{s}\) :

Concentration susceptibility

\(C_{\infty }\) :

Concentration outside the boundary layer

\(D_{m}\) :

Chemical molecular diffusivity

\(D_{f}\) :

Dufour number

\(g\) :

Gravitational acceleration

\({\text{Gr}}_{T}\) :

Local Grashof number for temperature

\({\text{Gr}}_{C}\) :

Local Grashof number for concentration

\({\text{Ha}}\) :

Hartmann number

\(K\) :

Stokes drag coefficient

\(\overline{K}\) :

Permeability constant

\(l\) :

Dust particle mass concentration

\({\text{Le}}\) :

Lewis number

\(N\) :

The number of dust particles

\(N_{1}\) :

Radiation parameter

\({\text{Pr}}\) :

Prandtl number

\(Q\) :

Volumetric rate of heat generation

\(q_{r}\) :

Radiative heat flux

\(R\) :

Suction/Injection parameter

\(R_{d}\) :

Non-dimensional Radiative heat flux

\(q_{r}\) :

Radiative heat flux

S r :

Soret number

\(T\) :

The temperature of the fluid

\(T_{0}\) :

Mean fluid temperature

\(T_{\infty }\) :

The temperature of the fluid outside the boundary layer

\(T_{p}\) :

The temperature of the dust particles

\(u,v\) :

Fluid velocity components in \(x,y\) directions

\(u_{p} ,v_{p}\) :

Velocity components of dust particles in \(x,y\) directions

\(x,y\) :

Cartesian coordinate system

\(\overline{\kappa }\) :

Thermal diffusion ratio

\(\kappa\) :

Thermal conductivity of the fluid

\( \kappa ^{\prime } \) :

Permeability constant

\(\kappa ^{\prime\prime}\) :

Rate of chemical reaction

\(\kappa_{1}\) :

Mean absorption coefficient

\(\sigma\) :

Electric conductivity

\(\sigma^{*}\) :

Stefan-Boltzmann constant

\(\gamma_{1}\) :

Chemical reaction parameter

\(\rho\) :

The density of the fluid

\(\rho_{p}\) :

The density of the dust particles

\(\lambda\) :

Heat generation or absorption

\(\theta\) :

Non-dimensional temperature for fluid

\(\theta_{p}\) :

Non-dimensional temperature for dust particles

\(\varphi\) :

Non-dimensional concentration for fluid

\(\varphi_{p}\) :

Non-dimensional temperature for dust particles

\(\beta\) :

Non-Newtonian Casson parameter

\(\beta_{T}\) :

Volumetric coefficient of thermal expansion

\(\beta_{C}\) :

Coefficient of concentration

\(\tau_{T}\) :

The relaxation time of the dust particles temperature

\(\tau_{v}\) :

The relaxation time of the dust particles velocity

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Authors and Affiliations

  1. Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

    Nepal Chandra Roy & Goutam Saha

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  1. Nepal Chandra Roy
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Correspondence to Nepal Chandra Roy.

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Roy, N.C., Saha, G. Heat and Mass Transfer of Dusty Casson Fluid over a Stretching Sheet. Arab J Sci Eng 47, 16091–16101 (2022). https://doi.org/10.1007/s13369-022-06854-x

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